Hard Nonlogarithmic Corrections of Order $m{\alpha }^7$ to Hyperfine Splitting in Positronium

Abstract

We consider hard three-loop nonlogarithmic corrections of order $m{\alpha }^7$ to hyperfine splitting in positronium. All these contributions are generated by the graphs with photon and/or electron loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams. The total result for all these diagrams is $\Delta E=-1.2917(1)m{\alpha }^7/{\pi }^3=-5.672$ kHz.

Comments: 10 pages, 8 fugures